檩条计算书一. 设计资料檩条采用中卷边C160x60x20x2.0截面，材料为Q235B；檩条跨度为5，檩条间距为1.5；跨度中央布置一道拉条；屋面的坡度角为5度；檩条按简支构件模型计算；屋面板与檩条连接的自攻螺丝直径为8mm；屋面板能阻止檩条的侧向失稳；二. 截面参数A(cm2)=6.07 e0(cm)=4.52I x(cm4)=236.59 i x(cm)=6.24W x(cm3)=29.57I y(cm4)=29.99 i y(cm)=2.22W y1(cm3)=16.19 W y2(cm3)=7.23I t(cm4)=0.0809 I w(cm6)=1596.28三. 荷载标准值恒载：面板自重: 0.3kN/m2檩条自重: 0.0892kN/m活载：屋面活载: 0.5kN/m2风载：基本风压: 0.35kN/m2体型系数-1.15，风压高度变化系数1风振系数为1；风压综合调整系数1.05；风载标准值：-1.15×1×1×1.05×0.35=-0.4226kN/m2；四. 强度校核恒载：q d=0.3×1.5+0.0892=0.5392kN/mM dx=0.125×0.5392×cos(0.08727)×5×5=1.679kN·mM dy=-0.125×0.5392×sin(0.08727)×(5/(1+1))2=-0.03671kN·m 活载：q l=0.5×1.5=0.75kN/mM lx=0.125×0.75×cos(0.08727)×5×5=2.335kN·mM ly=-0.125×0.75×sin(0.08727)×(5/(1+1))2=-0.05107kN·m 风载：q w=-0.4226×1.5=-0.6339kN/mM w=0.125×-0.6339×5×5=-1.981kN·mM x=1.2×1.679+1.4×2.335=5.283kN·mM y=1.2×-0.03671+1.4×-0.05107=-0.1156kN·m计算有效截面：B t=60/2=30H t=160/2=80计算上翼缘有效宽厚比：σ1=5.283/29.57×1e+3+(0.1156)/16.19×1e+3=185.8N/mm2（支承边）σ2=5.283/29.57×1e+3-(0.1156)/7.23×1e+3=162.681N/mm2（卷边边）α=(185.8-(162.681))/185.8=0.1244查表得：ξ=17∵B t≤100×(ξ/σmax)0.5=30.248，∴翼缘全截面有效！计算下翼缘有效宽厚比：σ1=-5.283/29.57×1e+3+(0.1156)/16.19×1e+3=-171.526N/mm2（支承边）σ2=-5.283/29.57×1e+3-(0.1156)/7.23×1e+3=-194.645N/mm2（卷边边）σ1≤0同时σ2≤0，翼缘受拉，全截面有效！计算腹板有效宽厚比：σ1=5.283/29.57×1e+3+(0.1156)/16.19×1e+3=185.8N/mm2σ2=-5.283/29.57×1e+3+(0.1156)/16.19×1e+3=-171.526N/mm2α=(185.8-(-171.526))/185.8=1.923查表可知腹板全截面有效！计算有效截面惯性模量计算可知：W ex=29.57cm3W ey1=16.19cm3W ey2=7.23cm3A e=6.07cm2截面考虑开洞影响，计算可知：W enx=29.249cm3W eny1=15.86cm3W eny2=7.083cm3A en=5.91cm2σ1=5.283/29.249×103+(0.1156)/15.86×103=187.91N/mm2σ2=5.283/29.249×103-(0.1156)/7.083×103=164.31N/mm2σ3=-5.283/29.249×103+(0.1156)/15.86×103=-173.339N/mm2σ4=-5.283/29.249×103-(0.1156)/7.083×103=-196.938N/mm2196.938<205，强度合格！五. 屋面板不能够阻止檩条的侧向失稳时的整稳验算屋面板能够阻止檩条的侧向失稳，可不予验算！六. 风吸力作用下受压下翼缘的整稳验算1 抗扭刚度C t计算C100=1700 Nm/m/radC t11=1700×(60/100)×(60/100)=612Nm/m/radC t12=130×3=390Nm/m/rad取C t1=C t11=612Nm/m/radC t2=4×206000×200000/1.5/1000/1000=109866.667Nm/m/radC t=1/(1/612+1/109866.667)=608.61Nm/m/rad2 考虑自由翼缘约束影响的修正系数η计算K=1/(4×(1-0.3×0.3)×160×160×(160+56.676)/206000/2/2/2+160×160/608.61)=0.01841x0=29.99/16.19×10=18.524mmI a=(160×2/3)×2×2×2/12+(160×2/3)×2×18.524×18.524=73272.263mm4I fly=(299899.998-73272.263)/2=113313.867mm4R=0.01841×2500×2500×2500×2500/3.142/3.142/3.142/3.142/206000/113313.867=0.3163 η=(1+0.0314×0.3163)/(1+0.396×0.3163)=0.89753 对主轴y－y的弯矩计算q=(-1.4×-0.4226×1.5-0.5392)=0.3483KN/mk=56.676/160=0.3542M x=0.3483×5×5×0.125×1000000=1088476.549NmmM y'=0.3483×0.3542×2.5×2.5×0.8975/8×1000000=86513.094Nmm4 W fly计算d1=29.99/16.19*10=18.524mmd2=29.99/7.23*10=41.48mmW fly1=113313.867/18.524=6117.211mm3W fly2=113313.867/41.48=2731.775mm3i fly=(113313.867/2/(160/6+20+60))0.5=23.047mm5 χ计算R0=0.01841*5000*5000*5000*5000/3.142/3.142/3.142/3.142/206000/113313.867=5.061 l fly=0.7*5000*(1+13.1*5.0611.6-0.125=1833.403mmλ1=3.142×(206000/235)0.5=93.014λfly=1833.403/23.047=79.551λn=79.551/93.014=0.8553φ=0.5×(1+0.21×(0.8553-0.2)+0.8553×0.8553)=0.9345χ=1/(0.9345+(0.9345×0.9345-0.8553×0.8553)0.5=0.76276 应力计算计算有效截面：B t=60/2=30H t=160/2=80计算上翼缘有效宽厚比：σ1=1.088/29.57×1e+3+(0.08651)/16.19×1e+3=42.154N/mm2（支承边）σ2=1.088/29.57×1e+3-(0.08651)/7.23×1e+3=24.844N/mm2（卷边边）α=(42.154-(24.844))/42.154=0.4106查表得：ξ=35.01∵B t≤100×(ξ/σmax)0.5=91.133，∴翼缘全截面有效！计算下翼缘有效宽厚比：σ1=-1.088/29.57×1e+3+(0.08651)/16.19×1e+3=-31.467N/mm2（支承边）σ2=-1.088/29.57×1e+3-(0.08651)/7.23×1e+3=-48.776N/mm2（卷边边）σ1≤0同时σ2≤0，翼缘受拉，全截面有效！计算腹板有效宽厚比：σ1=1.088/29.57×1e+3+(0.08651)/16.19×1e+3=42.154N/mm2σ2=-1.088/29.57×1e+3+(0.08651)/16.19×1e+3=-31.467N/mm2α=(42.154-(-31.467))/42.154=1.746查表可知腹板全截面有效！计算有效截面惯性模量计算可知：W ex=29.57cm3W ey1=16.19cm3W ey2=7.23cm3A e=6.07cm2W fly1=113313.867/18.524=6117.211mm3W fly2=113313.867/41.48=2731.775mm3σ1=1088476.549/0.7627/29570+86513.094/6117.211=62.409N/mm262.409<205，合格！七. 挠度q x=0.5392+0.75=1.289kN/mv=(5/384)×1.289×54×cos(0.08727)/20600/236.59×10000000=21.445mm21.445<33.333，合格！八. 长细比λx=5/6.24×100=80.12880.128<200，合格！λy=5/2.22/2×100=112.613112.613<200，合格！。